Convergence analysis of modulus-based matrix splitting iterative methods for implicit complementarity problems

An Wang; Yang Cao; Quan Shi

doi:10.1186/s13660-017-1593-7

Convergence analysis of modulus-based matrix splitting iterative methods for implicit complementarity problems

J Inequal Appl. 2018;2018(1):2. doi: 10.1186/s13660-017-1593-7. Epub 2018 Jan 3.

Authors

An Wang¹, Yang Cao², Quan Shi²

Affiliations

¹ 1School of Science, Nantong University, Nantong, 226019 China.
² 2School of Transportation, Nantong University, Nantong, 226019 China.

Abstract

In this paper, we demonstrate a complete version of the convergence theory of the modulus-based matrix splitting iteration methods for solving a class of implicit complementarity problems proposed by Hong and Li (Numer. Linear Algebra Appl. 23:629-641, 2016). New convergence conditions are presented when the system matrix is a positive-definite matrix and an [Formula: see text]-matrix, respectively.

Keywords: convergence; implicit complementarity problem; matrix splitting; modulus-based iterative method.